论文标题
银河系中心的超质量深色物体的紧凑性
Compactness of supermassive dark objects at galactic centers
论文作者
论文摘要
我们将重力镜头的紧凑性定义为无效的缩放接近距离（即$ r_0/m $）的最接近的距离，从而产生了图像。我们将40个超质量的深色物体建模为Schwarzschild镜头和计算镜头的紧凑性（由一阶相对论图像的形成决定）。然后，我们获得了一个新颖的公式，用于透镜的紧凑性随质量与距离比（$ m/d_d $）的函数以及镜头源与观察者源距离的比率（$ d_ {ds {ds}/d_s $）。该公式产生一个非常重要的结果：仅观察相对论图像将使透镜的物理紧凑度（半径与质量的比率）具有令人难以置信的准确上限，而没有任何了解镜头的质量，角度源位置，观察者 - 源和镜头和镜头的距离。同样，我们表明，对二阶相对论图像的观察将使上部紧凑度的上限较低。这些结果虽然用于银河系中心的超大质量黑物体，但对于任何足够紧凑的物体都可以产生相对论图像有效。
We define compactness of a gravitational lens as the scaled closest distance of approach (i.e., $r_0/M$) of the null geodesic giving rise to an image. We model forty supermassive dark objects as Schwarzschild lenses and compute compactness of lenses (determined by the formation of the first order relativistic image). We then obtain a novel formula for the compactness of a lens as a function of mass to the distance ratio ($M/D_d$) and the ratio of lens-source to the observer-source distances ($D_{ds}/D_s$). This formula yields a very important result: Just an observation of a relativistic image would give an incredibly accurate upper bound to the physical compactness (the ratio of the radius to mass) of the lens without having any knowledge of mass of the lens, angular source position, and observer-source and lens-source distances. Similarly, we show that the observation of the second order relativistic image would give a lower value of upper bound to the physical compactness. These results, though obtained for supermassive dark objects at galactic centers, are valid for any object compact enough to give rise to relativistic images.
